5. Concluding remarks

Let us summarize what we have said so far. Each bond portfolio BP (a human body? or a human body organ?) generates cash at various dates t1, t2, t3, …, tm. What should (could) be substituted for cash (payments generated by a BP) in the medical setting remains an important open problem. Maybe, it is something related to a human body's performance; call this mysterious agent by Z.

In bond portfolio theory, the greater payouts generated by BP, the higher is the present value (PV) and future value (FV) of BP. An analogous statement is therefore expected in the medical context. Having settled what is Z, it would be probably easy to find out what is the counterpart in medicine of the duration concept defined for the first time by Macaulay (in 1938) and independently by Redington (in 1952); see Formula (1).

Let us formulate the following hypothesis: the higher values (levels) of Z, the more healthy is a human body (a human body organ).

In the financial immunization context, there is a fixed date q when BP must attain at least a certain value L, called liability. In the medical context, one might say that there is a fixed date q when the quality of human health must attain at least a certain level L.

In the financial theory context, when interest rates s(t) change due to a shift a(t), that is, s tðÞ! s tð Þþ a tð Þ, then the FV of BP at date q may fall below L dollars. In the medical context, the appearance of disease may cause a deterioration of health at date q.

We still do not know what should (could) be substituted for interest rates s(t), knowing that changes (movements, shifts) in interest rates mean a disease.

Using the concept of duration (and dedicated duration), we identified the set IMMU of all shifts (diseases) a(t) against which BP is immunized. By means of notion of duration and convexity (dedicated convexity), we determined the best immunizing portfolios for a large class of shifts (continuous functions). In the financial context, the best portfolios meant portfolios generating the highest (unanticipated) rate of return. In the medical context, the best would probably mean the fastest rate of health improvement.
